Book:Frank Ayres, Jr./Theory and Problems of Differential and Integral Calculus/SI Edition

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Frank Ayres, Jr. and J.C. Ault: Theory and Problems of Differential and Integral Calculus (SI Edition)

Published $\text {1972}$, Schaum

ISBN 07 084395 3


Subject Matter


Contents

Preface to Second Edition (March 1964)
Chapter 1: Variables and Functions
Chapter 2: Limits
Chapter 3: Continuity
Chapter 4: The Derivative
Chapter 5: Differentiation of Algebraic Functions
Chapter 6: Implicit Differentiation
Chapter 7: Tangents and Normals
Chapter 8: Maximum and Minimum Values
Chapter 9: Applied Problems in Maxima and Minima
Chapter 10: Rectilinear and Circular Motion
Chapter 11: Related Rates
Chapter 12: Differentiation of Trigonometric Functions
Chapter 13: Differentiation of Inverse Trigonometric Functions
Chapter 14: Differentiation of Exponential and Logarithmic Functions
Chapter 15: Differentiation of Hyperbolic Functions
Chapter 16: Parametric Representation of Curves
Chapter 17: Curvature
Chapter 18: Plane Vectors
Chapter 19: Curvilinear Motion
Chapter 20: Polar Coordinates
Chapter 21: The Law of the Mean
Chapter 22: Indeterminate Forms
Chapter 23: Differentials
Chapter 24: Curve Tracing
Chapter 25: Fundamental Integration Formulas
Chapter 26: Integration by Parts
Chapter 27: Trigonometric Integrals
Chapter 28: Trigonometric Substitutions
Chapter 29: Integration by Parts
Chapter 30: Miscellaneous Substitutions
Chapter 31: Integration of Hyperbolic Functions
Chapter 32: Applications of Indefinite Integrals
Chapter 33: The Definite Integral
Chapter 34: Plane Areas by Integration
Chapter 35: Volumes of Solids of Revolution
Chapter 36: Volumes of Solids with Known Cross Sections
Chapter 37: Centroids
Chapter 38: Moments of Inertia
Chapter 39: Fluid Pressure
Chapter 40: Work
Chapter 41: Length of Arc
Chapter 42: Area of Surface of Revolution
Chapter 43: Centroid and Moment of Inertia
Chapter 44: Plane Area and Centroid of Area
Chapter 45: Length and Centroid of Arc. Area of Surface of Revolution
Chapter 46: Improper Integrals
Chapter 47: Infinite Sequences and Series
Chapter 48: Tests for Convergence and Divergence of Positive Series
Chapter 49: Series with Negative Terms
Chapter 50: Computation with Series
Chapter 51: Power Series
Chapter 52: Series Expansion of Functions
Chapter 53: Maclaurin's and Taylor's Formulas with Remainders
Chapter 54: Computations using Power Series
Chapter 55: Approximate Integration
Chapter 56: Partial Derivatives
Chapter 57: Total Differentials and Total Derivatives
Chapter 58: Implicit Functions
Chapter 59: Space Curves and Surfaces
Chapter 60: Directional Derivatives. Maximum and Minimum Values
Chapter 61: Space Vectors
Chapter 62: Vector Differentiation and Integration
Chapter 63: Double and Iterated Integrals
Chapter 64: Centroids and Moments of Inertia of Plane Areas
Chapter 65: Volume under a Surface. Double Integration
Chapter 66: Area of a Curved Surface. Double Integration
Chapter 67: Triple Integrals
Chapter 68: Masses of Variable Density
Chapter 69: Differential Equations
Chapter 70: Differential Equations of Order Two
INDEX


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